Instructions to Candidates
 This paper consists of two sections; Section I and Section II.
 Answer all the questions in Section I and any five questions from Section II
 Show all the steps in your calculations, giving your answers at each stage in the spaces provided below each question
 Marks may be given for correct working even if the answer is wrong.
 Nonprogrammable silent electronic calculators and KNEC Mathematical tables may be used, except where stated otherwise.
QUESTIONS
Section I (50 Marks)
Answer ALL questions in the section in the space provided:
 Evaluate without using a calculator 0.01% of . (3 marks)
 The sum of the ages of three brothers; Mike, Charles and Abdul is 65 years. Mike is twice as old as Abdul and one and half times as old as Charles. Determine their ages. (3 marks)
 A supermarket has 18 apples, 30 oranges and 54 apples. The fruits are to be arranged in rows such that every row contains same number of fruits of one type only. Determine the least number of rows required for this arrangement to happen. (3 marks)
 Find the area of the rectangle below. (3 marks)
 Without using a Calculator or Mathematical Table evaluate the value of p: (3 marks)
4/P^{2} =221^{2} 220^{2}  Calculate the value of x given that and AB= 5 units. (3 marks)
 Solve for k in the equation . (2 marks)
 Solve for x in the equation (3 marks)
 In the figure below ABF is a uniform cross section of a solid. AB, BC and BF are some of the visible edges of the solid. Complete the sketch showing the hidden edges with broken lines. (3 marks)
 Mr. Charles who deals in electronics sells a radio to a customer at Kshs. 1,440 after giving him a discount of 10% but finds that he still makes a 20% profit. Find the profit Mr. Charles would make if he does not give a discount. (3marks)
 The figure below shows a set of two right angled triangles ABD and BCD conjoined by side BD. Sides AB, BC and AD are 6cm, 5cm and 10cm in lengths respectively.
Calculate the size of angle CDB=t. (4 marks)  Given that log_{3}= 0.4771 and log_{5} = 0.6990, find without using Mathematical table or calculator log 0.045. (3 marks)
 Two towns A and B are 810km apart. A car left A at 8:00am moving towards B at an average speed of xkm/h. A bus left town B at 9:30am moving towards A at an average speed of 84km/h. Determine the average speed of the car, xkm/h, if the two vehicles met at 11.00am. (4 marks)
 In the figure given below, O is the centre of circle. If ∠BCA= 80º and ∠CB0= 10º.
Determine the size of ∠CAB. (3 marks)  Using midordinate rule with six strips estimate the area between the curve y=3x^{2}+4x+10, xaxis and the lines x=2 and x=4. (4 marks)
 Construct A'B'C'D' the image of quadrilateral ABCD below. Given that it undergoes under transformation enlargement with scale factor 2 and centre O. (3 marks)
Section II (50 Marks)
Answer ONLY FIVE questions in the section in the space provided:  The equation of line L_{1} is 2x+3y+ 6= 0.
 Find the gradient of line L_{1} (1 mark)
 The line l_{2} is perpendicular to l_{1} and passes through the point P with coordinates (7, 2), find the equation of l_{2} , giving the answer in the form y= mx+ c where m and c are constants. (3 marks)
 The line l_{1} and l_{2} intersect at point Q. Find the coordinates of Q. (3 marks)
 The line l_{3} is parallel to l1 and passes through point P. Find the equation of l3 giving the answer in the form ax+ by = c , where a , b and c are constants. (2 marks)
 Determine the x and yintercepts of the line l_{3}. (1 mark)
 The Form Two Parents of Ushindi High School decided to buy laboratory equipment worth Kshs.900,000 by each student contributing equal amount of money. Before they made the contribution 50 students got transferred to other institutions and this made the remaining students to pay Kshs.600 more.
 Taking to represent the original number of students, write down an expression for:
 The original contribution per student. (1 mark)
 The new contribution per student. (1 mark)
 Find the original number of students who were to contribute. (4 marks)
 Calculate the percentage change in the students’ contributions. (2 marks)
 If the ratio of boys to girls that remained in Form 2 was 13:12 calculate the amount contributed by the boys alone. (2 marks)
 Taking to represent the original number of students, write down an expression for:
 Two circles of radii 3.5 and 4.2 cm with centres O_{1} and O_{2} respectively intersect at points A and B as shown in the figure below. The distance between the two centres is 6 cm and the distance from O_{1} to the common chord AB along O_{1}O_{2} is x cm.
Calculate: The distance x cm to 3 decimal places. (3 marks)
 The size of ∠AO1B and ∠AO2 B (to the nearest degree). (3 marks)
 The area of quadrilateral O_{1}AO_{2}B, correct to 2 decimal place (2 marks)
 The shaded area correct to two significant figures. (Take. π=3.142). (2 marks)
 Three towns A, B and C are such that B is 120km on a bearing of 060º from A. C lies directly East of A on a bearing 165º from B. Using a scale of 1cm to represent 20km, a pair of compass and a ruler only, determine:
 the relative positions of A, B and C. (3 marks)
 drop a perpendicular from B to meet AC at M hence measure BM. (2 marks)
 construct a circle passing through the vertices A, B and C then calculate the area covered in the circle. (2 marks)
 Determine the amount of money used in ploughing the land inside the circle but outside triangle ABC at a rate of Kshs. 5000 per hectare. (3 marks)
 A solid is partly a cone and partly an hemisphere of radius 7cm. The slanting length of the cone is 25cm. Determine;
 the height of the solid. (2 marks)
 the volume of the solid (3 marks)
 the surface area of the solid. (3 marks)
 the mass of the solid if its density is 12.5g/cm3. (2 marks)
 In the figure below OB = b; OC = 3OB and OA = a
 Given that OD = 1/3OA and AN = 1/2AC, CD and AB and and meet at M. Determine in terms of a and b.
 AB
 CD
 Given that CM = kCD and AM = hAB. Determine the values of the scalars k and h. (5 marks)
 Show that O, M and N are collinear. (3 marks)
 Given that OD = 1/3OA and AN = 1/2AC, CD and AB and and meet at M. Determine in terms of a and b.
 The displacement of a particle is given as s=t^{3} 6t^{2}+9t+50 metres.
Determine; The displacement of the particle when t = 2 seconds. (2 marks)
 the velocity of the particle when t = 4 (2 marks)
 the acceleration of the particle when t = 5. (2 marks)
 the time when the particle is at rest. (2 marks)
 the displacement during the 3rd second. (2 marks)
 The height of a number of students was recorded in the table below. Each measurement is given to the nearest cm.
Height(cm)
Midpoint x
Frequency
138142
140
3
420
143147
8
148152
12
153157
20
158162
160
30
4800
163167
14
168173
7
173177
4
178182
180
2
360
∑f = ∑fx =  Complete the table. ` (3 marks)
 use the completed table to calculate the mean height of the students. (2 marks)
 Draw a histogram to represent the information. (2 marks)
 Use the histogram above to estimate the median height. (3 marks)
MARKING SCHEME

 M: C : A = 2x ; 3x ; 1.5x
x = 65/13
x = 5
mike's age = 30 years
charles age = 20 years
abdul's age = 15 years  18 = 2 x 3^{2}
30 = 2 x 3 x 5
54 = 2 x 3^{3}
gcd = 2 x 3
= 6
no of rows = 18/6 + 30/6 + 54/6
= 17  2x + 6 = x + 8
x = 2
L = 21 and W = 10
A = 21 x 10
= 210  4/p^{2} = (221  220)(221 + 220)
1/p^{2} = 441/4
1/p = ±21/2
p = ±2/21  AB = AO + OB
ans = x = 1 or 9  2k + 10 + 3k  20 = 90º
k = 20º  √2x  6 = 3 + x
2x  6 = x2 + 6x + 9
x2 + 8x + 15 = 0
x = 5 or 3  M.P. = 1440 x 100
90
= 1600
S.P = 1440 x 100
120
= 1200
profit = 1600  1200
= 400  BD = √10^{2} + 10^{2}
= 11.662
sin CDB = 5
11.662
= 28.209º  log 0.045 = log(3^{2} x 5 x 10^{3})
= 2log3 + log5 + log10^{3}
= 2 x 0.4771 + 0.6990 + 3
= 2.6532  The distance covered by the car by 9:30 am = 1.5xkm
Remaining distance = 810  1.5x
810  1.5x = 1.5
x + 84
810  1.5x = 1.5x + 126
x = 228  <OAC = <OCA = 70º and <OAB = 10º
<CAB = 70º + 10º
= 80º 
x 1.5 0.5 0.5 1.5 2.5 3.5 y 10.75 8.75 12.75 22.75 38.75 60.75
= 154.5 

 3y = 2x  6
y = 2/3x  2
m1 = 2/3  2/3 x m2 = 1
m2 = 1.5
y  2 = 1.5
x  7
y = 1.5x  8.5  at Q  2/3x  2 = 1.5x  8.5
x = 3
y = 2/3 x 3  2
=  4
hence the coordinates of is Q(3, 4)  m3 = 2/3
y  2 = 2
x  7 3
2x + 3y = 20  y intercept is 6^{2}/_{3} and x intercept is 10
 3y = 2x  6


 9000/x
 90000
x  50
 90000  90000 = 600
x  50 x
600x^{2}  30000x  45000000 = 0
x = 50 ± √2500 + 300000
2
= 50 ± 550
2
= 300 or  250
∴x = 300  original contribution = 900000/300
= 3000
%change = 600 x 100%
3000
= 20%  remaining students = 250
boys contributions = 130 x 3600
= 468 000


 scale diagram
 3.0 ± 0.1 cm
60 ± 2 km  radius 3.2 ± 0.1 cm
A = 22/7 x 64^{2}
= 12873.142857142 km^{2}  Area = 12873.142857142  1/2 x 120 x 60
= 9273.142857142
money spen = 9273.142857142 x 10^{6} x 5000
10^{4}
= kshs. 4636571429
 scale diagram

 h = 7 + √25^{2}  7^{2}
= 31 cm  v = 1/3 x 22/7 x 7^{2} x 24 + 2/3 x 22/7 x 7^{3}
= 1950^{2}/_{3}  S.A = 2 x 22/7 x 7^{2} + 22/7 x 7 x 2
= 858  m = 12.5 x 1950^{2}/_{3}
= 24383^{1}/_{3}g
 h = 7 + √25^{2}  7^{2}


 AB = a + b
 CD = 1/3a  3b
 k = 3/4 and h = 3/4
 OM = MN hence OM is parallel MN
Given OM is parallel MN and they share a common point M then points O, M and N are collinear


 S(2) = 2^{3}  6 x 2^{2} + 9 x 2 + 50
= 52  v = 3t^{2}  12t + 9
v = 3 x 4^{2}  12 x 4 + 9
= 9  a = 6t  12
when t = 5a = 6 x 5  12
a = 18  at rest v = 0
v = 3t^{2}  12t + 9 = 0
t = 1s or 3s  S(3rd) = 3^{3}  6 x 3^{2} + 9 x 3 + 50)  (2^{3}  6 x 2^{2} + 9 x 2 + 50)
= 2m
 S(2) = 2^{3}  6 x 2^{2} + 9 x 2 + 50


height (cm) midpoint (x) frequency (f) fx area cummulative area 138  142 140 3 420 15 15 143  147 145 8 1160 40 55 148  152 150 12 1800 60 115 153  157 155 20 3100 100 215 158  162 160 30 4800 150 365 163  167 165 14 2310 70 435 168  172 170 7 1190 35 470 173  177 175 4 700 20 490 178  182 180 2 360 10 500 Σf = 100 Σfx = 15840 
x = 15840/100
=158.4 cm 

1/2 cummulative area = 250
hence the median class is 138  162
30x = 250  215
x = 1^{1}/_{6}
median = 157.5 + 1^{1}/_{6}
= 158 ^{2}/_{3}

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